The strain and temperature scaling law for the critical current density of a jelly-roll Nb3Al strand in high magnetic fields
The strain and temperature scaling law for the critical current density of a jelly-roll Nb3Al strand in high magnetic fields
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DOI：
10.1088/0953-2048/15/7/301
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发表时间：
2002-07
影响因子：
3.6
通讯作者：
S. Keys;N. Koizumi;D. Hampshire
中科院分区：
文献类型：
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作者：
S. Keys;N. Koizumi;D. Hampshire
在B≤15T，4.2K≤T≤16K和−1.79%≤e≤+0.67%范围内，大量生产的Nb3Al多丝线材的工程临界电流密度(JE)和转变指数N(其中E=JN)被表征为磁场(B)、温度(T)和应变(E)的函数。通过互补电阻率测量直接确定上临界场(BC2(T，e))和临界温度(Tc(E))。定义在5%ρN、50%ρN或95%ρN的上临界场由经验关系bc2ρN(T，e)=bc2ρN(0，e)[1−(T/TCρN(E))ν]描述。当BC2ρN(0，e)≈3.6TCρN(E)−2 9.9时，ρN(0，e)是TCρN(E)的双值函数，但在零开尔文下的上临界场与临界温度成线性关系.乙脑被证实至少在−0.23%；e<；0.67%范围内是可逆的。使用体积钉扎力(FP)对JE数据进行了参数化，其中FP=JE×B=A(E)BC2n(T，e)BP(1−b)Q和b=B/BC2(T，e)。A(E)是应变的函数，当温度固定，应变变化时，FP的最大值(通过变场得到)是BC2的双值函数。为了达到磁体工程师(~1A)所要求的非常高的参数化精度，将数据划分为三个温度-应变范围，BC2(T，e)由经验关系和常数p，q，n和ν描述，应变相关变量A(E)，BC2(0，e)和TC(E)被视为自由参数并在每个范围内确定。通过使用5%ρN处的电阻率数据来约束Bc2(T，e)，也找到了描述大部分JE数据的单一标度律，其中ν=1.25，n=2.18，p=0.39和q=2.16。当Bc2(T，e)被约束在50%ρN或95%ρN时，标度律被破坏，使得p和q是温度的强函数，q也是应变的强函数。良好的标度为确定BC25%ρN(T，e)作为块体材料的特征(或平均)上临界场提供了支持。JE数据也符合仅包含基本常数的标度律，其形式类似于Kramer，其中金兹堡-朗道(GL)参数κ由关系式给出，γ为索末菲常数，t=T/TC(E)。当外加磁场等于由Kramer关系拟合出的上临界场时(即在BC2(T，e))，临界电流不为零，我们认为电流是渗流的。FP的泛函形式表明，在高场下，晶界钉扎并不限制JE，这与其他超导材料的JE-微结构关联是一致的。
The engineering critical current density (JE) and the index of transition, N (where E = αJN), of a Nb3Al multifilamentary strand, mass-produced as a part of the Fusion programme, have been characterized as a function of field (B), temperature (T) and strain (e) in the ranges B ≤ 15 T, 4.2 K ≤ T ≤ 16 K and −1.79% ≤ e ≤ +0.67%. Complementary resistivity measurements were taken to determine the upper critical field (BC2(T, e)) and the critical temperature (TC(e)) directly. The upper critical field defined at 5%ρN, 50%ρN or 95%ρN, is described by the empirical relation BC2ρN(T, e) = BC2ρN(0, e)[1 −(T/TCρN(e))ν]. The upper critical field at zero Kelvin and the critical temperature are linearly related where BC2ρN (0, e) ≈ 3.6TCρN (e) − 29.9, although strictly BC2ρN (0, e) is a double-valued function of TCρN (e). JE was confirmed to be reversible at least in the range −0.23% < e < 0.67%. The JE data have been parameterized using the volume pinning force (FP) where FP = JE × B = A(e)BC2n (T, e)bp (1 − b)q and b = B/BC2(T, e). A(e) is taken to be a function of strain otherwise the maximum value of FP (found by varying the field) was a double-valued function of BC2 when the temperature was fixed and the strain varied. To achieve a very high accuracy for the parameterization required by magnet engineers (~1 A), the data were divided into three temperature–strain ranges, BC2(T, e) described by the empirical relation and the constants p, q, n and ν and the strain-dependent variables A(e), BC2(0, e) and TC(e) treated as free-parameters and determined in each range. A single scaling law that describes most of the JE data has also been found by constraining BC2(T, e) using the resistivity data at 5%ρN where ν = 1.25, n = 2.18, p = 0.39 and q = 2.16. When BC2(T, e) is constrained at 50%ρN or 95%ρN, the scaling law breaks down such that p and q are strong functions of temperature and q is also a strong function of strain. Good scaling provides support for identifying BC25%ρN (T, e) as the characteristic (or average) upper critical field of the bulk material. The JE data are also consistent with a scaling law that incorporates fundamental constants alone, of the Kramer-like form where the Ginzburg–Landau (GL) parameter κ is given by the relation γ is the Sommerfeld constant and t = T/TC(e). At an applied field equal to the upper critical field found from fitting the Kramer dependence (i.e. at BC2(T, e)), the critical current is non-zero and we suggest that the current flow is percolative. The functional form of FP implies that in high fields the grain boundary pinning does not limit JE, this is consistent with JE-microstructure correlations in other superconducting materials.